A \(d\) -variate tropical polynomial \(f(x)\)  defines a function \(f:\mathbb {R}^d \rightarrow \mathbb {R}\)  that is a convex function, in that taking max and sum of convex functions preserves convexity [1]}. So, a tropical rational function \(f \oslash g:\mathbb {R}^d \rightarrow \mathbb {R}\)  is a difference of convex function [2]}, [3]}.
